Mathematical model.



A. H. WHEELER.

MATHEMATICAL MODEL.

APPLICATION FILED'SEPT- 3. 1914.

Patented July 25, 1916.

3 SHEETS-SHEET l m; NORRIS rnzns Cm, wAsHmamu. B4 c. r

A. H. WHEELER. MATHEMATICAL moon.

APPLICATION FILED SEPT- 3. I914.

Patented July 25, 1916.

3 SHEETS-SHEET 2.

TI'E NORRIS PETERS c0, WASHINGTON, D. c.

A. H. WHEELER.

MATHEMATICAL MODEL.

APPLICATION FILED SEPT- 3. 1914.

1 1 92,483. Patented July 25, 1916.

{SHEETS-SHEET 3.

Inventor THE NORRISPETERS cm, w/xgurmirou, n. c

ALBERT HARRY WHEELER, 0F WORCESTER, MASSACHUSETTS.

MATHEMATICAL 'MODEL.

Specification of Letters Patent.

Patented July 25, 1916.

Application filed September 3, 1914. Serial No. 860,041.

To all whom it may concern:

Be it known that I, ALBERT HARRY lVHEELEZi, a citizen of the UnitedStates, residing at lVorcester, in the county of Worcester and State ofMassachusetts, have invented a new and useful Mathematical Model, ofwhich the following is a specification.

My invention relates to improvements in mathematical models or the likein which skeleton-like or sectional forms of construction are providedwhich may be assembled or combined in a great variety of Ways to buildup or construct mathematical models of many interesting and importantforms and proportions which illustrate, represent, show and definemathematical and geometrical relations, proportions and forms and applyprinciples of mathematical, physical and mechanical sciences andsimplify their presentation and conception to the mind.

It relates, in particular, to the presentation and construction ofgeometrical forms and figures, of relations and principles ofgeographical and astronomical science, of natu'al crystalline forms andof certain conventional and symbolicalforms and figures which arecommonly applied and recognized in the arts and sciences.

In the mathematical sciences, in particular there are forms, relations,proportions, figures, diagrams and concepts in plane, solid, sphericaland special surface goemetries, of the conic sections and descriptivebranches of geometry and there are lines, points, surfaces and solids intheir individual and mutual relations which are difficult to represent,present to the mind or to conceive of or imagine, which by the means andmethods which I am about to explain and set forth may be readily,clearly and simply set forth, seen and understood.

My invention relates to certain methods and means for attaining suchresults by very easily constructed and simply. devised means which areinexpensive and may be produced in great quantities at very littleexpenditure of tune, material or cost.

The principal objects of my invention are these parts or blanks thatthey may be interchanged among themselves in a great variety of ways toproduce many variations in construction and form; to provide simple andefficient means for securing such parts or members together in engagedor interlocked position, either temporarily or permanently; to provideconstructions whereby alterations or variations in form may be easilyand directly obtained; to provide improvements in construction andmanufacture whereby the device may be efficient in operation, and can bemade in a very isimple manner; to provide means whereby, if desired, thedevice may be collapsed and made to assume flat or nearly fiat positionand thus may be carried around in very small compass; to provide simpleconstruction of relatively movable parts of such nature that the form orappearance of the device may be changed by moving the parts ormembersrelatively to each other; to provide convenient means for operating thesame; to provide means whereby additional parts may be easily introducedor old ones removed as may be desired; to provide means for receivingupon their surfaces numbers, letters, symbols or other suitabledistinguishable marks or entries of information which may be read andunderstood and utilized. to distinguish and designate parts or membersor regions of the same with reference to each other, or to indicateparts or members which may lie-brought into desired or properregistration, engagement or other relation with reference to each other,or to serve as means for indicating convenient or necessary order of en:gagement together or assembling together of parts to provide forparticular forms of constructions; to provide certain forms ofskeleton-like or sectional construction whereby all parts of theconstructed figure or model may be easily accessible and readilyinspected and examined; to provide locking devices whereby it will beimpossible for parts to become accidentally separated from each otherand displaced or lost.

Further objects and advantages of the. invention will appearhereinafter.

Reference is to be had to the accompanying drawings in which 1 Figure 11s a perspective view of a preshown in reduced scale.

fcrred form of the invention with three circula r parts or members shownin reduced scale as two circular blanks having certain openings orincisions therein. Figs. 3 and 5 are perspective "iews showing furthermodifications and the blanks with which they are constructed are shownin reduced scale. Fig. 1-. is a modified form shown in perspective. Fig.6 shows a more general modified form. Fig. 7 shows another modified formwith certain additional features and certain modifications of the blanksof which it is constructed shown in reduced scale. Fig. 8 shows anothermodified form. Fig. 9 shows a form of the invention shown in Fig. 1 incollapsed position and also shows an end or side View of the sameindicating the intersections of the collapsed nembers. Fig. 10 showsanother modified form of the inven tion in perspective. Fig. 11 shows aperspective view of the form of the invention shown in Fig. 10 but withthe addition of another part or member which envelops or incloses theparts shown in Fig. 10 in such a manner and method of construction asmay be adopted in many other forms'of the in vention but which is notshown in all. Fig. 12 shows a perspective view of the inclosing orenveloping or surrounding part or member of the invention which appearsin Fig.

, 11, but in this particular figure the enveloping or inclosing memberis shown as comprising or including within its boundaries the preferredform of the invention shown in Fig. 1. Fig. 13 is a perspective View ofa modified form of the invention but with the addition of certain. partsor members disposed or contained within the interior of the same in amanner which may be adopted in many of the forms of the invention butwhich is shown in a particular form in this figure. Fig. 15 is aperspective view of details of the parts or members included within andappearing in Fig. 13 and shows the manner or method by which they areengaged or may be engaged each with others and inclicates the method ofassembling the parts with each other. Fig. 1 1 is a perspective view ofa modified form of the invention with the addition of a modified form ofa part or member capable of certain motion with reference to other partsshown by means which will be described in detail. Fig. 16 is aperspective view of a preferred form of the invention like that shown inFig. 1 but showing by its position certain definite relations of theparts. Fig. 17 is a perspective View of the preferred form of theinvention such as is shown in Fig. 1, but

with additi ns... .A lank which shows the form and manner ofconstruction of one of the added members or parts is shown in reducedscale. Fig. 18 is a perspective view of a preferred form of theinvention as shown in Fig. 1 but with the inclusion within its boundaryof an assemblage of other additional members shown as assembledseparately in Fig. 19 and which parts are shown before being assembledas three circular blanks in reduced scale in Fig. 18.

Referring first to the preferred form shown in Fig. 1, a perspectiveview is shown of a model having a form which suggests, shows parts ofand defines a sphere in its geometrical form, determines the diameter ofthe same and shows lines upon the surface of the sphere defined andrelations between the same etc.

The blanks or parts which are assembled to form Fig. 1 are shown inreduced scale as three rings or portions of plane surfaces, 1, 2 and 3and which have a general circular outline or boundary.

It will be shown by reference to other figures that other and variousshapes and forms may be used to embody the improvements which I am aboutto explain and describe. In particular, certain blanks are shown in Fig.3 as having a general rectangular or squareoutline; in Fig. 6 thegeneral form of the blanks assembled is elliptic. In Fig. 10rectangular, circular and elliptic forms are shown, and it will bereadily understood that many alterations and variations are possible.

Certain of the curves, lines or boundaries as 4 in Fig. 1 will bereferred to hereinafter as being outer curves or boundaries, whilecertain other curves, lines or boundaries as 5 shown inFig. 1 will bereferred to as being 105 inner curves or boundaries. It will be seenthat if one of the blanks as 3 of Fig. 1 be caused to move or rotateabout an axis which may be taken as any diameter of one of the circles4: or 5, that the outer circle at will 110 generate, create or define byits rotation the surface of a sphere, while at the same time the innercurve or circle 5 will create, generate or define the surface of anothersphere which will lie within the surface of the, 1 5 sphere defined bythe rotation of the circle 1.

The blanks l, 2 and 3 have certain parts or portions cut away andremoved as shown at 6. Incisions, openings, cuts or slots 7 are madethrough the outer boundaries or curves of theblanks 1 and 2 as shown andthrough the inner boundaries or curves of the blank 3 as shown at 8, andthe regions of the blanks about or near these cuts, slots or openings asshown in the regions marked- 125 9 are left continuous and will bereferred to as tabs.

The blanks forming the model shown in Fig. 1 may be assembled asfollows: One of the blanks, as 1, may be placed, by slightly deformingits surface, within the opening 6 vof the blank 2, in such a way thatthe slots or openings 7 of 1 engage with the sur faces of the ring orblank 2, which surfaces are caused to pass within and through andbetween the incisions or slots 7. In this engaged position it will befound that either of the two engaged parts 1 or 2 may be rotated ormoved about the line of intersection or engagemgent with the othermember and may be brought into various angular positions with referenceto the same, and the members or blanks may thus be brought together inflat or nearly flat superposed position such as may be seen by referringto Fig. 9. When in such fiat superposed position, the slots 7 of theblank 2 which are not in engagement with the surfaces of the otherblank, 1, may be made to lie in close proximity to the same and when insuch po sition the third blank 3 may be readily passed over the twosuperposed blanks 1 and 2 in such a way that the slots or openings 8made within its surface may be made to engage with the superposedsurfaces of the blanks 1 and 2, and the slots or openings of the blank 3may be brought into engagement with the slots 7 of the blank 2, whichare not engaged otherwise. When in such position the members or blanks 1and 2 may be retated and separated in an angular sense about their lineof intersection passing through the slots 7 of the blank or member 1, insuch a way that the slots or openings 7 of one of them, as 2, engagewith and contain points of the surface of the member 3. Thus it may beseen that the slots or openings of the surface 1 may be made to engagewith points of the surface of the blank 2; the openings or slots of theblank 2 will engage with points of the surface of 3, and the openings orslots of 3 will in turn engage with points of the surface of the blank1, as shown in perspective View in Fig. 1. l urthermore, it will be seenand understood that when thus assembled, any one of the blanks may becaused to rotate about the line of engagement or intersection determinedby the slots or openings with which it engages with a second blank. Atthe same time the cuts or slots of the rotating blank may be made totravel along or to slide in contact with the surfaces and to assumedifferent positions with reference to the surfaces of the third blankwith which they engage. Thus each of the blanks has rotatable andslidable relations with reference to the other blanks with which it isassembled and engaged, and the three blanks may be brought into flat ornearly flat superposed collapsed position with reference to each other,as shown in Fig. 9.

Referring to Fig. 9, there will be seen at 10 a diagram which by theintersecting full lines crossing at the points marked 7 and 8 isintended to indicate the positions with reference to their superpositionof the blanks or members 1, 2 and 3 as seen when looking at theassembled blanks in the direction of the arrows 11 and toward the linepassing through the points a and y. The slots or openings 7 and 8 areshown as being terminated at their ends 12 by circular openings, enlarements or cross-cuts to prevent the further extension of the cuts oropenings 7 or 8 along the surfaces or within the body of the tabs ormaterial within and through which they are constructed and formed. Thus,means are provided to prevent the ac cidcntal tearing or wearing of theparts engaged.

Because of the fact that two of the blanks, such for example, as 1 and 2as shown in Fig. 1, are alike, it may be seen that either part may besubstituted for the other when making the assembled construction. Thatis, 1 may be first assembled within 2, or if desired, 2 may be firstassembled within 1.

Referring to Fig. 1, it will be seen that the outer boundaries 1, of theassembled sections or blanks generate by their rotation a surface whichin the figure shown is the surface of a sphere upon which lie as greatcircles the arcs of the outer boundaries 4: which generate it.Furthermore, a second spherical surface is generated or defined by therotation or movement of the inner curves or circles 5, and this innerspherical surface may be said to be defined by the arcs 5 which lie uponit. It will thus be seen that mechanical means have been provided forconstructing, showing and illustrating relations, proportions andproperties of geometrical and other mathematical forms.

In the preferred form shown in Fig. 1 there have been assembled twoso-called inner rings or members 1 and 2, and one so called outer ringor member 3, but this particular choice of parts is not essential as maybe seen by referring to Figs. 3, G, 8 and 10. Furthermore, it will befound possible to as semble together, if desired, three outside membersor blanks in such form as those shown in Fig. 1 and numbered 3.

In Fig. 2 is shown a modified form of the invention in which one outsidemember, such as the part numbered 3 in Fig. 1, is assem bled togetherwith two inner members having forms such as are shown in reduced scaleand are numbered 13 and 131. Slots, cuts or incisions 1% are made ofsuch a form that projecting parts or regions 15 referred to as teethproject across and interrupt the general normal course of opening of theslots or openings 1 1. These teeth 15 are adapted to engage with andpass through suitably formed and situated. openings or slots 16 in theouter member 3 with which the said member 13 engages as shown inperspective View in Fig. 2. The surfaces of the blanks parts or regionsof the surfaces cut by certam S shaped cuts or lnclslons 18 which formas shown pairs of teeth which are adapted and designed to engage withopenings or slots 19 as shown in Fig. 2.

It may be seen that the blanks or members 13 and 131 may be assembled bycausing the surfaces of the blank 13 to be inserted within and along theslot or opening 17 of the blank 131, and at the same time the surfacesof the member or part 131 to be inserted between and along the slot oropening 17 of the member 13 in such a way and to such an extent that the5 tabs or teeth of the blank 13 engage with and pass through the opening 19 of the blank 131, while the 8 tabs or teeth 18 of the blank 131enter, pass through and engage with the opening 19 of the other blank 13as shown in perspective View in Fig. 2. When thus assembled it will beseen that motion of rotation about the line of intersection of the partsor members 13 and 131, as determined by the line passing through the twosets of 8 tabs is possible, but lateral motion of the surfaces 13 and131 with reference to this same line is restricted by reason of theaction of engagement of the 8 tabs with the slots 19 through which theypass. It will be understood that these members 13 and 131 may be rotatedabout their line of intersection until they are in flat or nearly fiatsuperposed position with reference to each other, and when in suchposition the remaining part or member 3 may be assembled or engaged withthem in a manner similar to that described for Fig. 1.

It will be seen and understood that by suitably locating the positionsof the openings or slots 16 and the openings 14 and teeth 15 withreference to each other and to the line of intersection of the surfaces13 and 131, that any desired angular opening or inclination of the parts13 and 131 with reference to each other may be obtained and preserved.

Referring to Fig. 3, the method of assembling the separate members orblanks 20, 21 and 22 which are shown in reduced scale will be understoodby examining the perspective view shown, and by following the samegeneral methods and order of engagement of parts as has been alreadydescribed in detail with reference to other figures. V In particular, itwill be seen that in this particular form of the invention the blank 20may be placed within the opening 25 of the blank 21 in such a way thatthe slotsor incisions, 23, of 20, enter and engage with the slots orincisions of the blank 21. The collapsed blanks may then be placedwithin the opening 27 0f the blank 22 in such a way that the blank 20engages with and slides through the slot 28 of the blank 22, and theopenings, 26, of the part 21 engage with or interlock with the openings29 of the blank 22.

It will be understood from an examination of the perspective view ofFig. 3 that the surface of the sphere generated by and defined by theedges or boundaries, 30, of the assembled blanks, is in the sense withwhich the term was used in describing Fig. 1, an inner surface withreference to the material elements with which it is surrounded in partand by which it is in a sense defined as a mathematical surface.

The parts or members 32, 33 and 3%, as shown in Fig. 4: representassembled blanks which are essentially of circular outline or form andwhich are provided with openings within their interior regions and withcertain engaging and interlocking cuts or slots as shown. In particular,itwill be observed that certain of the engaged or interlocking slots oropenings, as those marked 35, are of the same general construction andproportion with reference to each other as are those which are numbered26 and 29 in Fig. 3.

It will be seen that the action of engagement of the slots at the pointsnumbered 36 serves to restrict the sliding motion of the surfacesthrough the slots with which they engage, but allows of unrestrictedmotion of rotation of the engaged surfaces about their line ofintersection passing through these points, 36. I

It will be seen and understood that Fig. 4 provides for features ofconstruction by which the functions of the tabs shown in Fig. 1 aretaken by the regions or parts of the surfaces in the neighborhood of theslots or cuts through which the intersecting surfaces pass.

While the forms of construction shown in Figs. 1, 2 and 4: are those ofspheres or spherical surfaces, I do not wish to be understood aslimiting myself to such restricted forms of construction.

An examination of Fig. 5 will show a modification of the generalconstruction shown in F ig. 3. In particulaiythe blanks 37, 38 and 39show in reduced scale elements of a general nature which relate them ina general way with the blanks shown in Fig. 3.

It will be seen that the perspective view shown in Fig. 5 suggests or ina sense defines by its edges an octahedron, and many interesting andimportant forms and figures may be built up and constructed by thegeneral means and methods shown and described.

Fig. 6 is a perspective view of an ellipsoid which possesses many of theelements of construction shown and described in the other figures. Theprojections or teeth 10 play the same part and have the same functionswith reference to the parts with which they are arranged as the Stabs orteeth, of Fig. 2, or the teeth,-, of Fig. 2 have with' suchas 3 of Fig.1and blanks ll and as shown in reduced scalein Fig. 7. It will beobserved with reference to Fig. 7 that the slots or openings intheblank'll are made in the opposite sense with referenc'eto simi larcuts or openings made in the blank 3 of Fig. 1. 1*urthermore, there ispresented in the blankflil a certain double construction of projectingparts or regions previously referred to as tabs.

In assembling the parts or members shown in Fig. 7 in perspective view,42 is first engaged within 41 and the two parts thus assembled a re thenengaged within the part or member, 3, as shown in Fig. 7 The assembledmembers are then securedin fixed relation with reference to rotationabout their common line of intersection by means of an additional member43, provided with slots or incisions suitably placed and adapted toengage with the projecting members or tabs of the assembled parts asshown at 44:.

In Fig. 8 the two scctional or skeleton parts or members 4-5 and 46 areadapted by means of slots or openings to engage along a line ofintersection passing through 47 and 'lS. The angle of inclination ofthis line of intersection with the slots or incisions 49 which are madein and through the members or parts is different from the angle madewith the slots 50 which are formed in and through the member 46. Thus,when the members 45 and 46 are rotated about their. 'hne of intersectionpassing through the points i? and 48, so as to lie in flat or nearlyflat position with reference to each other, the angles formed by thisline with the openings l9 and '50 will remain different, and as a resultthe parts or members 51 engaged with and passing through these slots or'openings 4!) and 50 will 'becaused to rotate and will be brought intoflat or nearly flat position with reference to each other and totheparts or members 4L5 and 4:6;

Figs. 10, 11 and 12 in which the parts shown in perspective areassembled to show and define certain elements of a cylinder and a.cylindrical surface. In particular, in. Fig. 11.0, the parts or members52 and 53 are shown as engaged with each other along a line ofintersection passing through the points 54 and 55 and the slots or cutsby which and with which the parts are engaged are shown by full anddotted lines. It will be understood by referring to the figure that theedges or boundaries such as those marked 56 sweep out or define by theirrotation or motion about the line of intersection of'vthe' surfaces 52and 53, cylindrical'sun faces. At the same time the parts ormembers-57and58 engagedwith the parts52 and 58 may be taken as defining the endsor bases of the cylinder.

In Fig. '10 it will be seentliat the angles of" inclination between theplane of the part59 and the line of intersection of the parts 52 and 53are different when measured in the planes of the parts'52 and 58. As aresult reference to each other, the part 59 will also be brought intoflat 0r nearly'flat position with reference to the same parts 52 and 53.The motions of the parts 57 and 58 as shown are not restricted in thesame way, but these parts or members as shown are free to be moved orrotated within certain limits while the remaining parts which areshownin the figure remain in flat or nearly fiat position with referenceto each other. Furthermore, it will be seen and understood by referringto Fig. '10 that when theparts or members 52 and 53 are inclined at anyspecified angle with reference to each other and their line ofintersection, the angles'of inclination of the parts 57, 58 and 59 withreference to each other and to the same line of intersection will bedetermined thereby.

It willbe recognized that great interest may be, aroused by the use ofsuch means and methods as I am now describing, and furthermore, it willbe possible to apply such means to many useful applications in the artsand sciences.

Fig. 11 is a perspective View of the form of the invention shown in Fig.10, but with the addition of an enveloping, inclosing'or surroundingmember or part 60, which may be taken as representing, showing ordefining the cylindrical surface of the cylinder,"

whereby it may be retained in position about such ino'losed orcontainedmembers as may be necessary for the purposes for which it is providedand intended. This part or member, 60, is provided with a slot oropening extending between, the points 61 and 62 throughwhich is passed apart or portion of its surface as shown in dotted lines surrounding inpart the regions 63 and '64. These parts or regions 63 and 64 may bedescribed in'a general way as consisting of a split'tab, the parts 63and 64 of which lie separated by a cut or incision extending from 65 to66 as shown." They are'further provided with cuts, or with slots oropenings or with such configuration of boundary that the distancebetween certain points as shown at 61 and 62 is lessthan the distancebetween other points as 67 and 68, when the tabs or regions 63 and 64lie in normal position with Thus, asshown, in

reference to each other. engaged position in Fig. 11 the portions orregions between the points 67 and 61, and between 68 and 62 formshoulders or checks which serve as means to prevent or to obtremeopposite edges or boundaries. of the in-.

closing or. surrounding part or member are shown by dotted lines 71 and72.

The function of the cut or incision from 65. to 66 is to provide meanswhereby the parts or inserted regions63 and 64 may by slightly deformingthe surfaces from their normal position withreference to each other bebrought together in partly overlapped position with reference to eachother, in such a manner and to such an extent that the extreme distancebetween the points 67 and 68 shall be not greater than the extreme orgreatest distance betweenthe ends 61 and 62 of the slot or openingthrough which they are intended and adapted topass and be inserted. Itwill be understood that when the points 67 and 68 of the shoulders ofthe regions or tabs 63 and 64 have passed through the slot 61 to 62 thatthe tabs or regions 63 and 64 may be caused or allowed to resume theirnormal positions with reference to eachother and to the line ofseparation between them in such a way thatthey no longer lie inoverlapped position with reference to each other. The restraining actionof the surfaces of the member 60 as exerted along the edges of the slotonopening from- 61 to 62 will be such asto tend to retain the insertedparts or members 63 and 64 in their normal position with reference toeach other and thus will serveto act to prevent or obstruct the removalorwithdrawal of the parts from engaged or interlocked position. 'It willbe understood that such a method of forming and securing in position anenveloping or inclosing member or part, maybe applied in a great varietyof ways to many forms of the invention. In

' particulan'it will be seen that in Fig. 12

the important andinteresting properties and relations existing between acylindrical surface and an inscribed sphere-is here sho wn.'.. Thepreferred form of the invention shown in Fig. 1 is here shown in fulland dotted,

lines and the inclosing, surrounding or (am veloping surface or part infull lines. Thus, I have-shown very definite relations which may be seento exist between the forms of the invention already described and itwill be understood that the elements of interchangeability or ofadditionof or of substitution of parts or members with reference to othersprovides means whereb-y'the general usefulness and practical applicationof the device to the uses for which it is adaptedand designed is greatlyincreased and extended.

In Fig. 13 is shown a somewhat modified form of the invention in whichthe parts are assembled to represent, suggest or define'a sphere. Theedges or inner boundaries 5 generate by their motion and hence define ina mathematical sense a spherical surface, which, with reference to theparts assembled, may be referred to as an inner spherical surface withinwhich is contained or inclosed, in part, a cylinder, suggested anddefined by certain added members or parts shown in the figure in fulland dotted lines. This cylinder is shown as beingcon= structed upon oneside of the member 73 and the details of its construction and the mannerof engagement of its parts is shown and suggested in Fig. 15. In Fig. 15the part 74 like numbered parts shown and described in Fig. 11. The cutsor separating incisions extending from 65 to 66 are shown in detail inFig. 15.

It will be observed that the method of assembling the parts-as shown inFig. 15 is somewhat difl'erent from that employed in the assembling oflike numbered parts in Fig. 11, in that the parts or members 76 and 77are engaged, each with the other, through and along the slots orincisions or openings extending from 65 to 66. Referring to Fig. 15 itwill be seen that the slots, openings or cuts extending from 61 to 62 inthe members 74 and 75 are designed and adapted to have the same relationto each other and to perform the same functions as like numbered partsshown and described in Fig. 11. There is, however, this importantdistinctionand difference, that in Fig. 11 all of the parts shown inthe-enveloping or inclosing member or part 60 are shown as existing andbeing formed in and out of the same surface or part, while in Fig. 15the parts described and shown are formed m,

1 through and out of different and separate members or parts 74;, 75, 76 and 77. I It will be seen, however, by referring to Fig. 13,

that when the assembled parts shown in detail in Fig. 15 are assembledas shown, that the parts or functions taken by the several regions,openings, cuts, tabs, etc., de

scribed, are, in general, the same as those shown and described indetail with reference to Fig. 11.

Referring to Fig. 15 it will be seen that the members 76 and 77 may becaused to rotate about their common line of intersection passing throughthe engaging slots and may thus be brought into flat or nearly flatsuperposed position with reference to each other.

Fig. 11 shows a perspective view of a modified form of the invention,representing, suggesting and defining a sphere. The parts or members 1and 3 as shown are similar to those designated by like numbers shown inthe preferred form in Fig. 1 and in other viewsfand the part 791 is ofthe same general form and construction as the part 73 shown in Fig. 13.It possesses, however, slightly different features in the details of itsconstruction. The member or part 7 8 shown in Fig. 14; is an additionalpart constructed from a blank or part having an essentially circularoutline or form. In Fig. 14, as shown, this part 78 is constructed froma blank of the same circular dimensions as the outer boundaries of theparts or members 1, 3 and 791. The blank is shown in Fig. 14: as beingfolded along certain lines issuing from the point 83 and passing throughcertain points 79, 80 and 81 of the outer boundary. Certain regions orportions of the surface of this blank are brought together andoverlapped as shown in Fig. 14. by the regions bounded by the points 79,80 and S3, and as suggested and shown in the figure by full and dottedlines. (through one of these overlapping regions or parts an incision,cut or slot, 85, is made as shown by full and dotted lines. Through thisincision or cut is caused to pass a suitably formed and situated tab orpart, 84, made by a suitably formed out or incision in the other of thetwo overlapping surfaces or parts. By suitably placing the incision orslot 85 and the engaging tab or tooth, 84:, with reference to each otherand to the sur faces in and with reference to which they are formed andconstructed, it may be seen that means are provided'for retaining theoverlapped or superposed surfaces in position of contact with eachother. Furthermore, it will be seen that the action of the free edge ofone of the overlapping parts or unlocking of the engaged or interlockedslot, 85,.with'the inserted tab, 81, and thus the member or part 7 8will be retained in its desired form of configuration as shown.Furthermore, it will be seen that because of the relations of size andshape of the parts 1, 3, 791 and 78that the outer boundaries ofthemember 7 8 passing through the points 79, 8O andSl maybe placed andretained in such a position as to be situated upon the surface of thesphere defined by the outer.

boundaries of the members 1, 3 and 791 as shown. If, now, the points 79,80 and 81 are placed at a radial distance from the cen ter of the spheredefined by the boundaries of 1, 3 and 791 equal to the radius of thesame sphere and are retained at the same radial distance from the samecentral point, then it willbe seen that tne points 7 9, 80 and 81 may becaused to move about upon the surface of the sphere and to occupydifferent positions upon the same.

By referring to. Fig. 14 it will be seen that one of thetwo overlappingregions or parts in contact within the region bounded by the points 79,80 and 83 is provided with an extended part or portion 86 shown'in fulland dotted lines. This tablike extension or part 86 is shown as beinginserted through a slot or opening 87 made in and through the member 791 beginning at the geometrical center in the figure shown at andextending therefrom in a radial direction. At a point inlits length,this opening, cut or slot is shown at 88 as being interrupted orobstructed with reference to its general direction by a member or partwhich normally projects across and obstructs the open ing in the sameway and manner as theteeth 15 in Fig. 2 or the 8 tabs in Fig. 2 obstructthe opening or slot through which they project. The inserted part ormember 86 is provided as shown in Fig. 14 with a suitable slot oropening through and with which the inserted tooth or tab 88 is shown asbeing inserted and engaged. It will thus be seen that means are providedfor retaining the inserted member 86 in engaged position with the member791.

By examining Fig. 14; it will be seen and understood that the sphericaltriangle suggested and defined by the arcs passing through the points79, S0 and 81 may be caused to move about and upon the surface of thesphere defined by the miter boundaries of the assembled members 1, 3 and791 and may be caused to take different positions thereon.

Fig. 1G is a perspective view of a preferred form of the invention soplaced that the points 89, 90 and 91 and their symmetrical points as 92,93 and 9-4; with reference to the center of the sphere may beconveniently seen. These sets of points determine with reference to thesurface of the sphere shown of which will now be described in detail.

The added part or member, 107, is provided at suitably situated pointsin its surface with openings, 108, through which pass and with whichengage or interlock certain members or parts, 109, which will bereferred to and described as supporting or connecting members. Thesesupporting or connecting members are caused to engage with and passthrough the openings 108 and also through other openings or incisions110 shown as being made inone of the members, 1, of the preferred formshown in Fig. 17. These supporting members are shown as beingstrengthened orrstiffened by being folded along their length andincisions or openings are made in and through their surfaces as shown inthe regions designated by the number 111. Means are thus provided forengaging the supporting members with the parts 107 and 1. The positionof the part 107 is determined and controlled by the construction andpositions of the supporting parts, 109, and by moving 1.07 withreference to the other assembled parts, the distance between 107 andother parts, such, for example as 1, may be made to change. It will beseen that by properly proportioning the parts that the outside member,107, may be caused to move with reference to the assembled parts shownin Fig. 17 as defining a sphere, so as to be at some time in theposition of a plane tangent to such a spherical surface.

In Fig. 17 there is also shown in reduced scale a blank or member, 112,which as shown has two openings or slots, 113, con} nectedby an incisionor cut made along the full line connecting the two slots and pass ingthrough the point ll i. The form of the blank shown in reduced scale inFig. 17 is somewhat similarto the form of one of the blanks shown inFig. 1, but there is this difference, that the blank shown in Fig. 17has a part of the boundary or outline shown as extending from andbetween the points designated by the number 116, a straight line whichis tangent to the circle which passes through other points of theboundary. If, now, the blank shown in Fig. 17 is bent or folded alongthe dotted line passing through the points 114 and 115, it may then beseen that it may easily and readily be assembled with and made to engagewith one of the members as 1, as shown in perspective view in Fig. 17This may be effected by causing certain regions of one of the parts, as1, to

enter and engage with the slots or openings, 113, as shown. It will thenbe seen that the region or part of the member 112 formed by the incisionor'cut, passing from one of the openings, 113, to the other and throughthe point, 114, acts as a restraining means to prevent the accidentaldisengagement of the parts 112 and l as shown.

If the blank shown in Fig. 17 in reduced scale be out along the dottedline, it may be seen that one or more of these parts shown as1117, ifdesired, may be assembled with the other parts as shown in theperspective view. When in such position it will be seen and understoodthat the lines or edges eX- tending between the points 115 and 116 maybe taken as suggesting and defining lines tangent to the sphere definedby the assembled parts, 1, 2 and 3, and by the means shown and describedthese lines passing through 115 may be moved about in the planedetermined and defined thereby. Furthermore, it Will be seen that theoutside member, 107, may be brought into the plane determined by thelines through 115 and its surface may be brought into contact with theseedges.

Fig. 18 is a perspective view of a preferred form of the inventionhaving included within its limits or boundaries certain additionalmembers or parts which are shown separately in assembled position inFig. 19 in perspective view. The three circular blanks shown in reducedscale in Fig. 18 are the parts or members which are assembled togetherto form the construction shown in Fig. 19. These blanks as shownconsistof three circular members having incisions or openings, 118 and 119,made therein in relatively opposite or contrary directions. They arereadily assembled by causing the slot or opening, 118, of one of them toenter and engage with the slot or opening 119 of a second blank, at thesame time causing the slot, 118, of the second 7 blank to enter theopening, 119, of the third blank and engage therewith, whilethe opening,118, of the third blank engages with the slot, 119', of the first blank.

In the description of the figures and draw ings it has been assumed,thus far, that the I have indicated a preferred order of assembling theparts by means of the Roman numerals, I, II, III, IV, V, VI, VII. Thesenumerals are employed to indicate and show that the parts or regionsnumbered I should first be brought together, then those successivelydesignated by the Roman numerals II, III, IV, etc., until, finally,those numbered VII are brought together. Thus it will be seen that theRoman numerals, I and II indicate the engagement of the member or part 2with the member, 1, by passing the regions of 2 designated by I and, IIthrough the slots of 1. designated by the same numerals I and IIrespectively. To bring the regions designated by the Roman numerals IIItogether, it is necessary to rotate the members 1 and 2 about their lineof engagement or intersection with each other into flat or nearly flatposition with reference to each other. The insertion of these collapsedparts within the openings or slots of the member, 3, is then indicatedby the Roman numerals IV and V. When in such inserted position theopening or separating apart of the assembled members required in orderto bring the regions designated by the Roman numerals VI and VIIrespectively into proximity, results in opening out the assembled partsinto the configuration of parts shOWn in perspective view in Fig. 1.

Roman numerals are used in other figures for similar purposes, such, forexample, as in Figs. 9, 10, 15, 16, 18 and 19, and in particular it willbe observed with reference to Fig. 10 that the numerals IV and XII arenot shown in this figure because of the fact that the points which theywould designate cannot be seen in the perspective view shown in Fig. 10,considered as being opaque.

Of course it will be understood that any sets or groups of symbols orcharacters which are recognized as occurring in some definite order ofsuccession may be used for the purpose for which the Roman numerals havejust been described as being applied.

I find it convenient also to use certain means for indicating ordesignating certain parts, portions or regions of the same or of two ormore members which are adapted to be brought together for the purpose ofassembling the same in some desired construe tion. I have accomplishedthis result by placing a group of three marks or dots as 7 three dotseach. in neighboring positions.

thereon are shown in perspective in Fig. 2.

Similar results may also be obtained by employing conventional orarbitrary symbols or marks or groups of such. Such means are employedand shown in Fig. 6 in which the two arbitrary signs I- and alsosimilarly disposed sets of three dots each are used. Similar means whichwill be readily recognized are used in other figures, such, for example,as in Figs. 14: and 17.

Certain regions or surfaces require to be overlapped or assembled andplaced in superposed position with reference to each other in order toeffect a desired construction or configuration of parts as in Fig. 1 1,in which it is necessary to place two surfaces or regions of surfacesincontact of super position in order to obtain a desired form ofconstruction. Greek letter delta A shown in full and dotted lines tosuggest or indicate that the regions on which these letters appearshould be brought together in contact as shown in the figure.

In Fig. 1, I have employed the letters A, B, C, etc. for the purpose ofindicating and designating certain regions or points of the assembledfigure. Thus convenient means are provided for referring to and pointingout relations and properties of the device in its assembled form.

Further reference to Fig. 1 will disclose another feature of myinvention which I will now describe.

It will be seen by referring to the blanks that the boundaries as shownin Fig. 1 are essentially circular but they are interrupted byprojecting regions or tabs and the circles forming the general outlinesof the same are interrupted at certain of these points. If,

now, lines be drawn across or upon the tabs as shown by the full linesin the regions of the tabs in Fig. 1, it will be seen that such lines asare drawn as shown serve to further define the circles which in partform the bounding edges of the several blanks shown.

A full line is shown as being drawn on the blank 112 in Fig. 17 to showthe relation I have used in Fig. 14 the between the straight edge of thesame with reference to its relation as being tangent to the circleforming the general circular outline of the blank as shown.

It will be understood that lines may be drawn upon the surfaces of thematerial of which the device described is constructed for the purpose ofshowing and defining many and various relations and properties thereof.

The invention has been shown and described as being built up andassembled of parts which are readily and directly adapted to beassembled and separated at will. possibility of use and operation isvery desirable and important, yet I realize that it may be-desirable toretain in assembled or V engaged relation. or position certain forms ofIassembled parts by means outside of themselves. Thus for example,members or partsmay be secured together permanently by gumming,sticking, pasting or causing shown and described capable of being easilyI the combination of three membersof. sheet;

constructed, assembled and preserved and are easily collapsed and may beconveniently kept andcarriedabout in small compass and bythemechanicalactionof their parts they are durable and adapted tomaintain desired configurations of parts, Also, because of certainelements. of interchangeability any i fe e ppli at ons may made withreference tothe. same part and combis nations of partsmay be devisedwhich Will result in the construction of a great number of differentforms and configurations from a. relatively smallnumber. of parts.

ile- I ha e u rat a d. des ibe a large number of modifications, I amaware hat ny; h n esmayrh made nv e nd. at any. ot e o ms: can benstructed that featuresofeach modifica: tion. may be applied to, otherswithin the re of his entiqaa expr s he claims. Therefore, I donot. Wishtobe lim e qa o e. for s s W but What: dq laim I 1 In a device of thecharacter described,

material having slits. for, receiving portions of each other andconnected together at the slits sothat eaehmember crosses one of theothers, one member being capable of rotatng u h a nslewi h espe t to asecond member ndepe ently e p sition of thethird mem e nd. Wi hout eomin gisengaged from either ofsaid other memg ers.

2. As anarticle of manufactur a model p ing a lur lity f m mbersotshematerial connected together so as to cross h ether nd d ne a y h n h mesion c rt Q ai membe s be ng providedwith slits for receiving portionsof another member and'bci ng movable on said other member, toward and;from eaeh other,

her by. a d other membe constitutes,

ui es. r. emi t 3- As a le Qf. ma ufacture, ma smatical model. of theclass described coming. rotatable'on an axis located in the plane I ofthesecond member, and the third member being rotatable on the second inall positions of the second member.

4. Asian article of'manufacture, a mathematical model comprising aplurality I of members formed of sheet material, said members havingslits at their edges, receiv ing each, others edges and constitutingguides for each, other, said members being rotatable relatively to eachother while connected together andguided by the slits.

5. As an article of manufacture, a mathematical model comprising aplurality of plane members of geometrical form, two of said membersbeing rotatable about an axis relatively to each other and both beingrotatable aboutsaid axis together relatively to a third, said memberseach having means for engaging and guiding the edge of one of the othermembers.

6. Asan article of manufacture, a mathematical model comprising threemembers of sheet material, said members having interengaging guides foreach other, certain of said members being relatively movable along saidguides, and also being independently rotatable about axes in their ownplanes.v

In a device of the character described,

the combination of three plane members,

certain of said members having their centers removed, whereby theinterior of the structure canbe observed, said members also having slitsat their edges constituting guides for each other, the edge of eachmember passing through and engaging with the slits of a secondrnember,theedges of which sec ond member passing through theslits in the thirdmember, while the edges of the third member pass through slits in thefirst member, whereby said parts are capable of motion relatively toeach other through the respective slits.

8. In a, device of the character described, the combination of threeplane members of a circular shape, certain of said members havingcentral circular openings therethrough, and said members being providedwith rad al sl ts extending through a space equal to the idth of themember between its outer edge andthe said central opening thereof, saidmembers all being of the same diameter, whereby one of said members cansaid members being provided with tabs each teedin ere he d of ne of a dslits.

9. In a device of the character described, the combination of threemembers of sheet material of a circular shape, provided with radialslits extending from their edges, said members all being of the samediameter, whereby the edge of one of said members can pass through theslits in another and have its outer edge register with the outer ends ofsaid slits, said members being connected around one end of each slit.

10. In a device of the character described, the combination of aplurality of plane members, said members having slits therein extendingfrom the defining edges thereof, the edges of each member extendingthrough the slits of another member and movable in said slits,-ccrtainof said members being adapted to have their relations of engagementrelative to each other. interchanged so that instead of one of saidmembers engag ing in slits of the second the second may be arranged toengage in slits of the first.

11. In a device of the character described, the combination of threeintegral plane members connected together so that each one crosses bothof the others and having slits for receiving each others edges slidably,said members being assembled together to define a body having threedimensions and being collapsible flatwise into substantially the sameplane.

12. In a device of the character described, the combination of aplurality of integral plane members connected together so that each onecrosses both of the others, and means whereby one member is capable ofrotating about a central axis located in the plane of one of the othermembers without becoming disengaged from either of said other members,said members being provided with designating characters located adjacentto the points at which they cross each other for convenience inassembling.

13. As an article of manufacture, a model comprising a plurality ofmembers of sheet material, one of said members having a slit extendingfrom its edge, through which another of said members movably passes, thefirst named member being provided with a projecting tab extending aroundthe end of the slit and connecting the material on opposite sides of theslit.

14. As an article of manufacture, a model comprising a plurality ofmembers of sheet material, one of said members having a slit extendingfrom its edge and of a length sub stantially equal to the width of thatmember, and having an integral tab extending around the end of the slitto hold the two parts on opposite sides of the slit together, another ofsaid members passing into the slit.

15. As an article of manufacture, a model comprising a plurality ofmembers of sheet material, one of said members having a pair of slitsextending from its edges and another one of said members extending intosaid slits, said slits being so arranged relatively to each other thatmotion of the second mem' ber away from the other in one direction isarrested by the end of one slit and motion away in another direction isarrested by the end of another slit.

16. As an article of manufacture, a model comprising a plurality ofmembers of sheet material, one of said members having a pair ofoppositely located slits in alinement with each other but extending inopposite directions from heir closed ends, another of said membersextending into said slits at its opposite edges, whereby the secondmember cannot be removed from the first member except by motion in adirection parallel to the plane thereof without distortion of one ofsaid members.

17. As an article of manufacture, a model comprising a plurality ofmembers of sheet material, one of said members having slits, another ofsaid members extending into said slits whereby the slits constituteguides for the second member and the second member constitutes guidesfor the slitted member, said slits being arranged to prevent removal ofthe second member from the first member except by motion in a directionparallel to the plane thereof Without distortion of one of said members.

18. As an article of manufacture, a model comprising a plurality ofmembers of sheet material, one of said members having means for holdinganother and preventing their separation without distortion, said meanscomprising slits for receiving the edges of the other member, said twomembers being connected with a third member and being movable togetherwith respect to it.

19. As an article of manufacture, a model formed of sheet material andhaving an incision therethrough, two projections extending into andthrough said incision in the same plane and abutting against each otherinsaid incision, and together filling the in cision length-wise thereof.

20. In a device of the character described, the combination of aplurality of members of sheet material having slits receiving portionsof each other, whereby said members said members having incisionstherethrongh Intestimony whereof I have hereunto set extending first onone side and then on the my hand, in the presence of two subscribingother side of a line so as to produce tWo tabs Witnesses.

extending in opposite directions from the ALBERT HARRY WHEELER. saidline and another of said members hav- Witnesses:

ing a slit therein for receiving said tabs ALBERT ALPHEUs WHEELER,

from opposite sides thereof. HELEN MARION WHEELER.

Copies of this patent may be obtained'for five cents each, by addressingthe Commissioner of ratentl, Washington, D. C."

